Pro-EU politicians say the plan represents the worst of scenarios, a point underscored on Friday when Jo Johnson resigned as transport minister, calling the deal offered a choice between “vassalage and chaos” and demanding a second referendum.

On the other side, Brexit backers want a clean break with the EU so Britain can strike new trade deals. Northern Irish members of parliament (MPs) fear the province will end up being treated differently than the rest of Britain.

In a joint opinion piece for The Sunday Telegraph newspaper, Tory Brexiteer Steve Baker and Sammy Wilson, Brexit spokesman for the Democratic Unionists – the Northern Irish party that props up the Conservatives in Parliament – vowed to reject the deal unless Mrs May backs down.

“We do not wish to see ‘no deal’ with our EU partners. We share the prime minister’s ambition for an EU free-trade agreement, but not at any price and certainly not at the price of our Union,” the pair wrote. “If the government makes the historic mistake of prioritising placating the EU over establishing an independent and whole UK, then regrettably we must vote against the deal.”

One area of contention centres on efforts to introduce a review clause into the divorce treaty to make sure the Irish issue doesn’t keep the UK locked in the EU’s trading regime indefinitely. Brexiteers insist Britain must be able to leave any customs arrangement.

“It cannot be a decision that can be overturned by the European Union; it must be capable for the United Kingdom to decide to leave that customs arrangement and it cannot be something the European Union can hold us to,” Andrea Leadsom, the Brexit-backing leader of the House of Commons, told BBC Radio 5 Live on Sunday.

The resignation of Mr Johnson last week came four months after his more famous brother, arch-Brexiteer Boris Johnson, quit as foreign secretary over the direction of Brexit. Four more pro-EU ministers are “on the brink” of resignation, The Sunday Times reported.

Navigating Brexit is scarcely less difficult for the opposition Labour Party, as many of its MPs represent districts that voted to leave the EU in the 2016 referendum.

Labour has said it wants a general election rather than a second Brexit referendum if Mrs May’s plan is rejected. Writing in The Sunday Times, Labour’s Brexit spokesman Keir Starmer said there was no duty on politicians to surrender to a bad deal for fear crashing out of the bloc in March.